# Why the Fermi temperature isn't zero?

The fermi temperature is defined as $$k_BT_f = E_f$$

But the fermi energy is the energy at $T=0$, where the energy level is the highest occupied for electrons. So, why is the fermi temperature defined as $\neq 0$?, What temperature $T_f$ is measured? Over who is T measured?

• Possible duplicate: physics.stackexchange.com/q/216207/5963 – Harry Johnston Apr 16 '18 at 2:59
• I also read that question, but I still do not understand at all, why fermi temperature is so high ? Are $T_f$ and $T$ related? – PCat27 Apr 16 '18 at 3:07
• I think Rob's answer addresses that - if I'm reading it correctly, $T_f$ is not actually the temperature of anything in particular, but it can be useful to compare the Fermi temperature to the actual temperature of the system. I may be mistaken; I'm not personally familiar with the concept. – Harry Johnston Apr 16 '18 at 3:16

The temperature is set to zero to define Fermi energy because $T=0$ corresponds to the ground state of this electronic system. The electrons are still moving around with their zero-point motion, and the Fermi temperature corresponds to this motion. Considering that electrons don't contribute much to the heat capacity of a bulk material, the electrons can have relatively high kinetic energies without appreciably raising the temperature of the total system.